The present disclosure relates generally to graphical models, and more specifically, to reasoning over cyclical directed graphical models.
Graphical models are widely used in machine learning to represent the patterns of dependence between variables and to predict the probability of some variables given some other variables. In addition, graphical models are often used in artificial intelligence to perform causal inference and social network analysis. When deploying a graphical model, there is a basic choice of representation between undirected models and directed models. In general, while undirected models are more robust, they often allow less powerful inference when compared to directed models. Though directed models can support more powerful inference, there are often more constraints on their application. One such constraint is that most directed models must be acyclic, that is, it must not be possible to trace a path from a node back to itself by following directed edges in the graph. A Bayesian network is an example of a directed graphical model that must be acyclic. The restriction that a Bayesian network must be acyclic significantly reduces the applicability of Bayesian networks, especially in applications such as unstructured information processing where graphs are likely to have cycles because the data is noisy or incomplete. This is a loss because Bayesian networks are often significantly more expressive than their undirected counterparts.